6533b7dafe1ef96bd126eb52

RESEARCH PRODUCT

A note on the analytic solutions of the Camassa-Holm equation

Maria Carmela LombardoMarco SammartinoVincenzo Sciacca

subject

Partial differential equationCamassa–Holm equationFunction spaceComplex singularitieMathematical analysisGeneral MedicineNonlinear Sciences::Exactly Solvable and Integrable SystemsCauchy–Kowalewski TheoremCamassa–Holm equationAnalytic solutionAnalytic functionMathematicsMathematical physicsSign (mathematics)

description

Abstract In this Note we are concerned with the well-posedness of the Camassa–Holm equation in analytic function spaces. Using the Abstract Cauchy–Kowalewski Theorem we prove that the Camassa–Holm equation admits, locally in time, a unique analytic solution. Moreover, if the initial data is real analytic, belongs to H s ( R ) with s > 3 / 2 , ‖ u 0 ‖ L 1 ∞ and u 0 − u 0 x x does not change sign, we prove that the solution stays analytic globally in time. To cite this article: M.C. Lombardo et al., C. R. Acad. Sci. Paris, Ser. I 341 (2005).

yearjournalcountryeditionlanguage
2005-12-01
10.1016/j.crma.2005.10.006http://hdl.handle.net/10447/7197